Recent developments of multi-scale meshfree methods and their applications
in mechanics are surveyed. Three major methodologies and their applications
are given. First, meshfree Galerkin methods, which have been an active
research area in recent years, are reviewed. Second,
multiresolution analysis is introduced and integrated within a meshfree
approach. The resulting multiple scale meshfree method is called the Reproducing
Kernel Particle Method (RKPM). Third, concurrent and hierarchical bridging
scale methods are proposed for multi-scale analysis of fracture. The focus
of this presentation is placed on simulations of finite deformation fracture;
shear bands; and nano-scale mechanics. As a nanoscale system, single walled
carbon nanotubes (SWCNT) have a number of likely applications based on
their outstanding physical and chemical
properties, and size and shape, suggesting their eventual role in lightweight,
high-strength materials, and in molecular electronics as both devices and
nanowires. Several computer simulations of the mechanics of nanotubes are
given.
Dr. Wing Kam Liu received his B.S. with highest honor from the University
of Illinois at Chicago (1976); his M.S. (1977) and Ph.D.(1981) from Caltech.
His research activities include development of finite element and meshfree
methods, concurrent and hierarchical bridging scale methods, molecular
dynamics, and multi-scale analysis. Liu's honors include the Gustus L.
Larson Memorial Award (1995), the Pi Tau Sigma Gold Medal (1985) and the
Melville Medal (1979), all from the ASME; the Thomas J. Jaeger Prize (1989)
given by the International Association for Structural Mechanics in Reactor
Technology, the Computational Structural Mechanics Award (2001) from the
U.S. Association for Computational Mechanics (USACM), and the American
Society of Automotive Engineers' Ralph R. Teetor Educational Award (1983).
Liu serves on the executive committee of the ASME applied mechanics division.
He is currently the president of
USACM. |